In a conventional MRI system, one often acquires image data in a two-dimensional variable space called k-space. The present state of the art steps through each line of k-space by stepping through a sequence of gradient fields. To acquire the entire 2D data set, one must acquire a set of lines in k-space. Since there is a different sequence of gradient fields for each line of k-space, this can be a time-consuming process.
It is known that by encoding image data in a spatially-periodic encoding field, one can accelerate the image acquisition. Such spatially-periodic fields are sinusoidal, and hence periodic, along one spatial dimension, e.g. x, and vary linearly in the orthogonal spatial dimension, e.g. y. These fields have come to be known as “PERL” fields (“PERiodic in x and Linear in y”).
U.S. Pat. No. 5,365,172 to Hrovat, et al., the contents of which are herein incorporated by reference, discloses a method and system for using a PERL field to acquire image data and for processing that data to reconstruct an image. However, although Hrovat teaches methods for reconstructing the encoded image, those methods rely primarily on numerical methods for inverting an integral transform.